<div class="swiper">
  <div class="swiper-wrapper">
    <div class="swiper-slide">
      <div class="slide-img"><img src="images/swiper_img_01.jpg" alt=""></div>
      <div class="slide-content">
        <h1 class="from_top">Slide Title 01</h1><!-- アニメーションを適用 -->
        <p>Lorem ipsum dolor sit amet, consectetur</p>
        <div class="caption">caption 01</div>
      </div>
    </div>
    <div class="swiper-slide">
      <div class="slide-img"><img src="images/swiper_img_02.jpg" alt=""></div>
      <div class="slide-content">
        <h2 class="from_left">Slide Title 02</h2><!-- アニメーションを適用 -->
        <p class="from_right">Ipsa, quis ex repudiandae eum </p><!-- アニメーションを適用 -->
        <div class="caption">caption 02</div>
      </div>
    </div>
    <div class="swiper-slide">
      <div class="slide-img"><img src="images/swiper_img_03.jpg" alt=""></div>
      <div class="slide-content">
        <h3 class="from_bottom">Slide Title 03</h3><!-- アニメーションを適用 -->
        <p>Ullam rerum quasi libero esse </p>
        <div class="caption">caption 03</div>
      </div>
    </div>
  </div>
  <div class="swiper-pagination swiper-pagination-white"></div>
  <div class="swiper-button-prev"></div>
  <div class="swiper-button-next"></div>
</div>

.slide-img img {
  width: 100%;
}
.swiper-slide .slide-content h1, .swiper-slide .slide-content h2, .swiper-slide .slide-content h3 {
  position: absolute;
  top: 20%;
  left: 50%;
  transform: translate(-50%, -50%);
  color: #FFF;
  font-size: 30px;
  text-shadow: 2px 2px rgba(0,0,0,0.3);
}
.swiper-slide .slide-content p {
  position: absolute;
  top: 50%;
  left: 50%;
  transform: translate(-50%, -50%);
  color: #FFF;
  text-shadow: .5px .5px rgba(0,0,0,0.6);
  margin: 0;
  padding: 0;
  font-size: 18px;
}
.swiper-slide .slide-content .caption {
  position: absolute;
  bottom: 30px;
  right: 30px;
  color: #FFF;
  font-size: 16px;
  background-color: rgba(0,127,127,0.5);
  padding: 3px 8px;
}

/* 以下追加（変更）部分 */
@keyframes fromTop {
  0% {
    top: 0%;
    opacity: 0;
  }
  100% {
    top: 20%;
    opacity: 1;
  }
}  
  
@keyframes fromBottom {
  0% {
    top: 80%;
    opacity: 0;
  }
  100% {
    top: 20%;
    opacity: 1;
  }
}  

@keyframes fromleft {
  0% {
    left: 0%;
    opacity: 0;
  }
  100% {
    left: 50%;
    opacity: 1;
  }
}
  
@keyframes fromRight {
  0% {
    left: 100%;
    opacity: 0;
  }
  100% {
    left: 50%;
    opacity: 1;
  }
}
 
/* .from_top を指定した要素のアニメーション */
.swiper-slide-active .from_top {
  animation: fromTop .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_bottom を指定した要素のアニメーション */
.swiper-slide-active .from_bottom {
  animation: fromBottom .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_left を指定した要素のアニメーション */
.swiper-slide-active .from_left {
  animation: fromleft .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_right を指定した要素のアニメーション */
.swiper-slide-active .from_right{
  animation: fromRight .6s ease-in-out .5s 1 normal both;
} 

<script>
  let mySwiper = new Swiper ('.swiper', {
    loop: true,
    
    pagination: {
      el: '.swiper-pagination',
      clickable: true,
    },

    navigation: {
      nextEl: '.swiper-button-next',
      prevEl: '.swiper-button-prev',
    },

  })
</script>